Presents two solutions of the Isis Problem, finding the dimensions of a rectangle for which the numerical values of the area and perimeter are equal, to hypothesize how the ancient Egyptians may have solved the problem without the benefits of more modern mathematics. (MDH)

Discusses possible solutions for the problem of determining how many sandwiches were made with specific ingredients that appeared in the March 1998 issue of this journal. (ASK)

Describes the results of part of a study into mathematical problem solving in secondary schools. Concludes that positive results were achieved, in part, as a consequence of the time that was spent in problem-solving lessons which allowed students to practice reading and working with word problems and working on basic material, particularly…

Shares some explorations of Fibonacci sequences with a special focus on problem-solving and posing processes. (ASK)

Presents a problem that uses the design show and asks students to find a series of moves to take the design from the top-left corner of a piece of paper to the bottom-right corner while remaining in its original orientation. (ASK)

Presents answers to the problem appearing in the January, 1999 Problem Solvers section of this journal, which was a strategy game called "Take Two" in which two players played by placing seven chips in a row and removing one or two chips each turn. (ASK)

The mathematical depth that is potentially present, even in simple problems is illustrated. An extended analysis of a problem that is an analysis from a mature mathematical perspective with careful attention paid to mathematical reasoning and to using good mathematical habits of mind is used.

In this paper we describe an ontological and semiotic model for mathematical knowledge, using elementary combinatorics as an example. We then apply this model to analyze the solving process of some combinatorial problems by students with high mathematical training, and show its utility in providing a semiotic explanation for the difficulty of…

In university mathematics courses, the activity of proof construction can be viewed as a problem-solving task in which the prover is asked to form a logical justification demonstrating that a given statement must be true. The purposes of this paper are to describe some of the different types of reasoning and problem-solving processes used by…

This descriptive study was aimed at looking into how Primary 5 pupils solve pre-algebra problems concerning patterns and unknown quantities. Specifically, objectives of this study were to describe Primary 5 pupils' solution strategies, modes of representations and justifications in: (a) discovering, describing and using numerical and geometrical…

Many states have begun the process of developing or adapting English Language Proficiency (ELP) standards to align with the Common Core State Standards (CCSS) and the forthcoming Next Generation Science Standards (NGSS). This need stems not only from a desire to ensure that "all" students receive the rigorous and systematic education…

The goal of the two Power of Data (POD) projects was to increase science, technology and math skills through the implementation of project-based learning modules that teach students how to solve problems through data collection and analysis utilizing geospatial technologies. Professional development institutes in two formats were offered to…

The conference of which these are the proceedings was held in June-July 1982 at Williams College in Williamstown, Massachusetts. The purpose was to discuss the restructuring of the first two years of college mathematics to provide some balance between the traditional calculus-linear algebra sequence, and discrete mathematics. The volume contains…

This manual is used with MATHBOXES, a computer program written for Apple II microcomputers to help children relate formal mathematical symbols for representing simple word problems to the informal strategies using physical objects that they naturally use to solve them. There is a substantial body of research that documents that young children are…

This collection of reprints from the IDEAS section of the "Arithmetic Teacher," has been selected from those activities appropriate for students in grades 4 through 8. The selections have been reprinted just as they originally appeared in the journal. The ideas are grouped under the headings computation, fractions, problem solving, geometry, and…